However, if \(A\subset X\)  is noncompact, \(\breve{\mathcal {E}}^+_A\)  is no longer vaguely compact, and the infimum in (REF )
is in general not attained among the admissible measures — even for a perfect kernel.
To overcome this inconvenience, Fuglede has formulated the (dual) minimum energy problem over the class \(\Gamma _A\subset \mathcal {E}\)  (see below), which leads to the same concept of inner capacity, but it is already solvable (see [1]}).
